Shortcut to chemically accurate quantum computing via density-based basis-set correction.

Using GPU-accelerated state-vector emulation, we propose to embed a quantum computing ansatz into density-functional theory via density-based basis-set corrections to obtain quantitative quantum-chemistry results on molecules that would otherwise require brute-force quantum calculations using hundreds of logical qubits. Indeed, accessing a quantitative description of chemical systems while minimizing quantum resources is an essential challenge given the limited qubit capabilities of current quantum processors. We provide a shortcut towards chemically accurate quantum computations by approaching the complete-basis-set limit through coupling the density-based basis-set corrections approach, applied to any given variational ansatz, to an on-the-fly crafting of basis sets specifically adapted to a given system and user-defined qubit budget.

Accelerated basis-set convergence of coupled-cluster excitation energies using the density-based basis-set correction method.

We present the first application to real molecular systems of the recently proposed linear-response theory for the density-based basis-set correction method [, , 234107 (2023)]. We apply this approach to accelerate the basis-set convergence of excitation energies in the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) method. We use an approximate linear-response framework that neglects the second-order derivative of the basis-set correction density functional and consists in simply adding to the usual Hamiltonian the one-electron potential generated by the first-order derivative of the functional.

A density-fitting implementation of the density-based basis-set correction method.

This work reports an efficient density-fitting implementation of the density-based basis-set correction (DBBSC) method in the MOLPRO software. This method consists in correcting the energy calculated by a wave-function method with a given basis set by an adapted basis-set correction density functional incorporating the short-range electron correlation effects missing in the basis set, resulting in an accelerated convergence to the complete-basis-set limit. Different basis-set correction density-functional approximations are explored and the complementary-auxiliary-basis-set single-excitation correction is added.

Effective quantum electrodynamics: One-dimensional model of the relativistic hydrogen-like atom.

We consider a one-dimensional effective quantum electrodynamics (QED) model of the relativistic hydrogen-like atom using delta-potential interactions. We discuss the general exact theory and the Hartree-Fock approximation. The present one-dimensional effective QED model shares the essential physical feature of the three-dimensional theory: the nuclear charge polarizes the vacuum state (creation of electron-positron pairs), which results in a QED Lamb-type shift of the bound-state energy.

Basis-set correction based on density-functional theory: Linear-response formalism for excited-state energies.

The basis-set correction method based on density-functional theory consists in correcting the energy calculated by a wave-function method with a given basis set by a density functional. This basis-set correction density functional incorporates the short-range electron correlation effects missing in the basis set. This results in accelerated basis convergences of ground-state energies to the complete-basis-set limit.

Photoionization and core resonances from range-separated time-dependent density-functional theory for open-shell states: Example of the lithium atom.

We consider the calculations of photoionization spectra and core resonances of open-shell systems using range-separated time-dependent density-functional theory. Specifically, we use the time-dependent range-separated hybrid (TDRSH) scheme, combining a long-range Hartree-Fock exchange potential and kernel with a short-range potential and kernel from a local density-functional approximation, and the time-dependent locally range-separated hybrid (TDLRSH) scheme, which uses a local range-separation parameter. To efficiently perform the calculations, we formulate a spin-unrestricted linear-response Sternheimer approach in a non-orthogonal B-spline basis set using appropriate frequency-dependent boundary conditions.

Systematic lowering of the scaling of Monte Carlo calculations by partitioning and subsampling.

We propose to compute physical properties by Monte Carlo calculations using conditional expectation values. The latter are obtained on top of the usual Monte Carlo sampling by partitioning the physical space in several subspaces or fragments, and subsampling each fragment (i.e.

Photoionization and core resonances from range-separated density-functional theory: General formalism and example of the beryllium atom.

We explore the merits of linear-response range-separated time-dependent density-functional theory (TDDFT) for the calculation of photoionization spectra. We consider two variants of range-separated TDDFT, namely, the time-dependent range-separated hybrid (TDRSH) scheme, which uses a global range-separation parameter, and the time-dependent locally range-separated hybrid (TDLRSH), which uses a local range-separation parameter, and compare with standard time-dependent local-density approximation (TDLDA) and time-dependent Hartree-Fock (TDHF). We show how to calculate photoionization spectra with these methods using the Sternheimer approach formulated in a non-orthogonal B-spline basis set with appropriate frequency-dependent boundary conditions.

Basis-set correction for coupled-cluster estimation of dipole moments.

The present work proposes an approach to obtain a basis-set correction based on density-functional theory (DFT) for the computation of molecular properties in wave-function theory (WFT). This approach allows one to accelerate the basis-set convergence of any energy derivative of a non-variational WFT method, generalizing previous works on the DFT-based basis-set correction where either only ground-state energies could be computed with non-variational wave functions [Loos et al., J.

Basis-set correction based on density-functional theory: Rigorous framework for a one-dimensional model.

We re-examine the recently introduced basis-set correction theory based on density-functional theory, which consists of correcting the basis-set incompleteness error of wave-function methods using a density functional. We use a one-dimensional model Hamiltonian with delta-potential interactions, which has the advantage of making easier to perform a more systematic analysis than for three-dimensional Coulombic systems while keeping the essence of the slow basis convergence problem of wave-function methods. We provide some mathematical details about the theory and propose a new variant of basis-set correction, which has the advantage of being suited to the development of an adapted local-density approximation.

Accurate energies of transition metal atoms, ions, and monoxides using selected configuration interaction and density-based basis-set corrections.

The semistochastic heat-bath configuration interaction method is a selected configuration interaction plus perturbation theory method that has provided near-full configuration interaction (FCI) levels of accuracy for many systems with both single- and multi-reference character. However, obtaining accurate energies in the complete basis-set limit is hindered by the slow convergence of the FCI energy with respect to basis size. Here, we show that the recently developed basis-set correction method based on range-separated density functional theory can be used to significantly speed up basis-set convergence in SHCI calculations.

Self-consistent density-based basis-set correction: How much do we lower total energies and improve dipole moments?

This work provides a self-consistent extension of the recently proposed density-based basis-set correction method for wave function electronic-structure calculations [E. Giner et al., J.

Almost exact energies for the Gaussian-2 set with the semistochastic heat-bath configuration interaction method.

The recently developed semistochastic heat-bath configuration interaction (SHCI) method is a systematically improvable selected configuration interaction plus perturbation theory method capable of giving essentially exact energies for larger systems than is possible with other such methods. We compute SHCI atomization energies for 55 molecules that have been used as a test set in prior studies because their atomization energies are known from experiment. Basis sets from cc-pVDZ to cc-pV5Z are used, totaling up to 500 orbitals and a Hilbert space of 10 Slater determinants for the largest molecules.

Relativistic short-range exchange energy functionals beyond the local-density approximation.

We develop relativistic short-range exchange energy functionals for four-component relativistic range-separated density-functional theory using a Dirac-Coulomb Hamiltonian in the no-pair approximation. We show how to improve the short-range local-density approximation exchange functional for large range-separation parameters by using the on-top exchange pair density as a new variable. We also develop a relativistic short-range generalized-gradient approximation exchange functional that further increases the accuracy for small range-separation parameters.

A basis-set error correction based on density-functional theory for strongly correlated molecular systems.

We extend to strongly correlated molecular systems the recently introduced basis-set incompleteness correction based on density-functional theory (DFT) [E. Giner et al., J.

Density-Based Basis-Set Incompleteness Correction for Methods.

Similar to other electron correlation methods, many-body perturbation theory methods based on Green's functions, such as the so-called approximation, suffer from the usual slow convergence of energetic properties with respect to the size of the one-electron basis set. This displeasing feature is due to the lack of explicit electron-electron terms modeling the infamous Kato electron-electron cusp and the correlation Coulomb hole around it. Here, we propose a computationally efficient density-based basis-set correction based on short-range correlation density functionals which significantly speeds up the convergence of energetics toward the complete basis set limit.

Self-Consistent Range-Separated Density-Functional Theory with Second-Order Perturbative Correction via the Optimized-Effective-Potential Method.

We extend the range-separated double-hybrid RSH+MP2 method (Ángyán, J. G.; et al.

Chemically accurate excitation energies with small basis sets.

By combining extrapolated selected configuration interaction (sCI) energies obtained with the Configuration Interaction using a Perturbative Selection made Iteratively algorithm with the recently proposed short-range density-functional correction for basis-set incompleteness [E. Giner et al., J.

Asymptotic behavior of the Hartree-exchange and correlation potentials in ensemble density functional theory.

We report on previously unnoticed features of the exact Hartree-exchange and correlation potentials for atoms and ions treated via ensemble density functional theory, demonstrated on fractional ions of Li, C, and F. We show that these potentials, when treated separately, can reach non-vanishing asymptotic constant values in the outer region of spherical, spin unpolarized atoms. In the next leading order, the potentials resemble Coulomb potentials created by effective charges which have the peculiarity of not behaving as piecewise constants as a function of the electron number.

Range-separated double-hybrid density-functional theory with coupled-cluster and random-phase approximations.

We construct range-separated double-hybrid (RSDH) schemes which combine coupled-cluster or random-phase approximations (RPAs) with a density functional based on a two-parameter Coulomb-attenuating-method-like decomposition of the electron-electron interaction. We find that the addition of a fraction of short-range electron-electron interaction in the wave-function part of the calculation is globally beneficial for the RSDH scheme involving a variant of the RPA with exchange terms. Even though the latter scheme is globally as accurate as the corresponding scheme employing only second-order Møller-Plesset perturbation theory for atomization energies, reaction barrier heights, and weak intermolecular interactions of small molecules, it is more accurate for the more complicated case of the benzene dimer in the stacked configuration.

Linear-response range-separated density-functional theory for atomic photoexcitation and photoionization spectra.

We investigate the performance of the range-separated hybrid (RSH) scheme, which combines long-range Hartree-Fock (HF) and a short-range density-functional approximation (DFA), for calculating the photoexcitation/photoionization spectra of the H and He atoms, using a B-spline basis set in order to correctly describe the continuum part of the spectra. The study of these simple systems allows us to quantify the influence on the spectra of the errors coming from the short-range exchange-correlation DFA and from the missing long-range correlation in the RSH scheme. We study the differences using the long-range HF exchange (nonlocal) potential and the long-range exact exchange (local) potential.

A Density-Based Basis-Set Correction for Wave Function Theory.

We report a universal density-based basis-set incompleteness correction that can be applied to any wave function method. This correction, which appropriately vanishes in the complete basis-set (CBS) limit, relies on short-range correlation density functionals (with multideterminant reference) from range-separated density-functional theory (RS-DFT) to estimate the basis-set incompleteness error. Contrary to conventional RS-DFT schemes that require an ad hoc range-separation parameter μ, the key ingredient here is a range-separation function μ(r) that automatically adapts to the spatial nonhomogeneity of the basis-set incompleteness error.

Quantum Package 2.0: An Open-Source Determinant-Driven Suite of Programs.

Quantum chemistry is a discipline which relies heavily on very expensive numerical computations. The scaling of correlated wave function methods lies, in their standard implementation, between and , where N is proportional to the system size. Therefore, performing accurate calculations on chemically meaningful systems requires (i) approximations that can lower the computational scaling and (ii) efficient implementations that take advantage of modern massively parallel architectures.

A formally exact one-frequency-only Bethe-Salpeter-like equation. Similarities and differences between GW+BSE and self-consistent RPA.

A formally exact Bethe-Salpeter-like equation for the linear-response function is introduced with a kernel which depends only on the one frequency of the applied field. This is in contrast with the standard Bethe-Salpeter equation (BSE) which involves multiple-frequency integrals over the kernel and response functions. From the one-frequency kernel, known approximations are straightforwardly recovered.